Hyperfine tensor relations

An unambiguous identification of anomalous muonium with the bond-center site became possible based on pseudopotential-spin-density-functional calculations (Van de Walle, 1990). For an axially symmetric defect such as anomalous muonium the hyperfine tensor can be written in terms of an isotropic and an anisotropic hyperfine interaction. The isotropic part (labeled a) is related to the spin density at the nucleus, ip(0) [2 it is often compared to the corresponding value in vacuum, leading to the ratio i7s = a/Afee = j i (O) Hi/) / (O) vac- The anisotropic part (labeled b) describes the p-like contribution to the defect wave function. 

To determine static properties of the SeO radical in KDP and DKDP, the temperature dependence of the hyperfine interaction between unpaired electron and Se (I = 1/2) nucleus was measured [53]. The hyperfine tensor component A, where the direction is along the c-axis, shows an isotope effect, because its value is higher in DKDP than in KDP. Furthermore, its value shows a jump at Tc for DKDP and a considerable temperature dependence in the PE phase of both crystals, approximated by the relation A (T) = A (0) - B coth(ro/T), where To 570 K for both crystals. It is interesting to note that A, similarly to the As NQR frequency and P isotropic chemical shift, should be constant in the PE phase if the two-state order-disorder mechanism of the corresponding tetrahedron holds. However, while the temperature dependencies of the As NQR frequency and P isotropic chemical shift in the PE phase were explained as originating from a six-state order-disorder mechanism [42] and additional displacive mechanism [46], respectively, here it was assumed that excitation of some extra lattice vibration mode with frequency Tq affects the hyperfine tensor components and causes the temperature dependence of A. ... 

The calculation of magnetic parameters such as the hyperfine coupling constants and g-factors for oligonuclear clusters is of fundamental importance as a tool for the evaluation of spectroscopic data from EPR and ENDOR experiments. The hyperfine interaction is experimentally interpreted with the spin Hamiltonian (SH) H = S - A-1, where S is the fictitious, electron spin operator related to the ground state of the cluster, A is the hyperfine tensor, and I is the nuclear spin operator. Consequently, it is... 

From these results one can see the incredible power of the combined EPR/ENDOR experiment. While the EPR spectrum of irradiate adenosine had rather narrow lines, the spectrum was unresolved due to the overlap of several radicals. The ENDOR spectra were easy to follow for complete rotations about all three crystallographic axes. Analysis of the ENDOR data yielded accurate anisotropic hyperfine tensors that could be related to two different free radicals. From these results one can confidently say that Radical I is the N3 protonated adenine anion A(N3+H) and Radical II is the N6 deprotonated adenine cation A(N6-H) With ENDOR data one is able to determine the protonation state of a radical, and if care is taken in the analysis, to even discern slight deviations from planarity of radicals. 

Figure 11 The magnetic field dependence of H-ESEEM spectra obtained for Fe(II)NO-TauD samples treated with aKG and taurine deuterated at both Cl andC2. Data were obtained using the ratio method described for Figure 9. The field positions displayed are (a) 172.8 mT (b) IQO.OmT (c) 290.0mT and (d) 345.0 mT. Simulated H-ESEEM spectra (dashed lines) for the Ci,C2-deuterated taurine are plotted along with the data. For the stronger coupled Ci deuteron, Hamiltonian parameters identical to those of Figure 10 were used. Hamiltonian parameters used for a second deuteron on C2 were principal deuteriiun hyperfine values, —0.13, —0.13, 0.26 MHz Euler angles for hyperfine tensor, 0, 63°, 0 e q Q, 0.20 MHz q, 0 and Euler angles relating nqi to hyperfine, 0, 23°, 0...

Here we have separated the isotropic and magnetic dipolar parts hence Tnuv denotes the part of the hyperfine tensor containing the anisotropic components. The hyperfine tensor TNuv is related to the reduced hyperfine tensor ANuv in Eqn. (1) by... 

The study of radicals trapped in single crystals of their precursors has shown that the hyperfine tensors for both a- and j9-fluorine atoms are much more anisotropic than the tensors for related a- and jS-hydrogen atoms. This feature is well illustrated for the a-atoms by the observations for monofluoroacetamide radical, XXIV, shown in Table 10. 

With these technical prerequisites fulfilled it is perhaps surprising that the complete information about the electronic and structural parameters of the interaction of the unpaired metal ion electron with nuclei in their immediate coordination environment is still rarely exploited. One reason may be attributed to the samples themselves. The information about the g- and the hyperfine tensor(s) as primary parameters obtained by EPR/ENDOR requires, basically, single crystals as samples more precisely, single crystals for which a high-resolution structure is available. Only then can the tensor directions that are measured experimentally with respect to the crystal morphology be related, by transformation, with the molecular structure. There are, however, only a few examples of such studies in the literature [2,3]. Often, single crystals of proteins cannot be crystallized in a size sufficient for... 

Suppose that one has extracted a (e.g., proton) hyperfine tensor from orientation-selective ENDOR measurements. How can this information be utilized in terms of relation to structural and electronic properties First, it has to be emphasized that the hyperfine tensor is established within the framework of the ordiogo-nal axes of the g-tensor. If it is possible to assign the hyperfine tensor within a protein prosthetic group to a specific proton, at the same time the g-tensor with respect to the molecular frame is fixed. This is important information that is otherwise only obtained from single-crystal measurements. 

The components of the total hyperfine tensor. A, observed in the ESR spectra, are obtained by adding Ajso to the Txx, Tyy, and components, respectively, of the dipolar tensor. For molecules with a well-defined axial symmetry it is common to report just one value of the dipolar hf tensor, Adip. This is related to the largest dipolar component (here assumed to be Tk), as Adip = 1 /2 It is also useful to compute the values perpendicular and parallel to a particular bond (here assumed to be along the z-axis). 

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